All right, let's see if I can help you with this. I do like the idea of further exploration of the Old Chateau, first off. It is creepy and full of mysteries, and while they were intentionally left unexplained so that they would be creepy, I do love a good fan theory about this sort of thing. (And I hope Gardenia's okay... I like her. :p) It should be very interesting.
Now... Detective PC? That's a bit of an odd name. Are those initials? First and last name? Or is he just one of those few people who's named something like TJ without it really meaning anything? PC isn't a terrible name or nickname on its own, but just be careful before--it's using the same acronym as "personal computer", "political correctness" or even "PokéCommunity", and those were what sprang to mind when I first saw it. I guess even TJ could stand for something completely unrelated to "Tim Junior" or whatever, but it's certainly not as common as "PC". Something that is more immediately recognizable as a name and not as a desktop computer might be a wiser choice if you aren't already dead-set on using it. (If you are, then perhaps you can have some characters mock his name in the story?)
I would be careful with your description of PC. That basic appearance and outfit, combined with you outright mentioning that you were inspired by the AA series (you have good taste in games, by the way), makes it seem just a little like you're trying to find a way to fit Phoenix himself into a Pokémon story. Taking a little inspiration from his character/design is no problem, but do be sure that he's not a carbon copy of Nick that's been shoved into Eterna City just because.
Is Gardenia PC's mother, or is her disappearance possibly related to his mother's earlier disappearance? When I first skimmed this a while ago, intending to come back later, I thought that they were two distinct events, but now I read it again and it looks like you might only be talking about one mystery. Which is it?
Perhaps the most confusing, and I apologize now because this is where I'm going to get long-winded, is the fact that he's already a detective at the age of seventeen. I bet people would underestimate him due to his age... especially because there's really no precedent for someone that young ever becoming a detective. Detective work, while not quite on the same level as being a beat cop out on the streets at night, is complicated, taxing and dangerous. Detective is actually usually a promotion from beat cop/officer, at least in the US--the police prefer it if you've had several years' worth of prior experience enforcing law out on the streets, and somehow I doubt they'd have a fifteen-year-old beat cop waving a gun and running around after criminals who also have guns. If he was never a beat cop then he'd have to get the requisite experience from someplace else, and again, where can he plausibly get that at such a young age?
...I mean, I guess you could make the argument that if they trust ten-year-olds with freaking charizard and aggron (not to get into the whole "waaah ten is too early" debate) then it's not totally unreasonable that people in the Pokémon world could start looking for real jobs at an earlier age than they normally do in the real world. Even so, I'm still having trouble swallowing someone that young intentionally being sent out to chase dangerous criminals, or being trusted to logically solve complicated things like murders.
And believe me, I know just how awkward it is--I'm actually writing a story that involves a lot of police officers and some private investigators, and I've been doing a ton of research to make sure I'm writing them believably. One of my detectives is sixteen, and there's a nineteen-year-old who just made sergeant (at least a rank above detective in many jurisdictions, although seeing as detective is usually optional this particular character skipped it). And it is killing me that they are so young. My problem is that I'm writing an alternate universe story and working with pre-established characters. While the entire thing is supposed to be silly as a rule (and so I guess it's not a huge problem that they're severely underage, as the story isn't meant to be taken entirely seriously) it just doesn't feel right to alter their ages on top of all the other sacrilege I'm committing. So I'm having to come up with all sorts of excuses and explanations for why Emil shows up out of nowhere and makes detective at like fifteen (without even serving as a beat cop as far as they know!) and how an idiot like Lloyd could ever scrape a promotion to sergeant or how on earth he even got out of the police academy in the first place, and it is hard.
You aren't limited by the ages and abilities of canon characters. You're making this character up on your own, and therefore you have the freedom to tweak either him or his job so that they mesh properly and are at least somewhat credible to your readers, even if his coworkers doubt him. The obvious answer to your believability problem is to make PC older than seventeen. I'd say at least twenty and with some exemplary work as a beat cop, although if that were the case then I'd think more people would see him as capable of being a good detective because he's already proven himself as an officer of the law prior to his promotion.
The other answer is not to have him be an official police detective (or even private investigator, which doesn't require police experience but is generally a field people enter after several years of studying criminal justice or serving as a lawyer), but to have him be what is called an "amateur detective", like Agatha Christie's Miss Marple or, to give a more modern example, Lawrence Block's Bernie Rhodenbarr. As the term implies, they aren't police detectives. They're Egyptologists, bookstore owners, chefs, dog breeders, even unassuming little old ladies. But as their rotten luck would have it, they keep stumbling onto twisted mystery after twisted mystery. It takes what wit they have and whatever parts of their non-detective skill set come in handy ("Hah! I can prove that this Egyptian artifact is a forgery, which in turn incriminates This Person!"), or perhaps just their "normal person's perspective" and ability to see other things that the police might miss, to solve the crime and save the day. If you make PC an amateur detective then him being younger is suddenly a lot more believable. It's one thing to have a prodigious young character, but it's something else entirely to have the police trusting someone who is still ultimately a child to solve murders for them.
Now, maybe you have a reason for PC being hired as a detective at such a young age--there are tons of children's stories and movies out there, for example, that have underage detectives or spies or what have you. But it's explicitly stated that there is a special reason that these characters are chosen when an adult, who would presumably be stronger, more mature, more intelligent and more generally reliable, would have been the logical choice otherwise. You haven't made it clear that there is such a reason, though, and so if you want PC to be young and a police detective/private eye then you'll have to make sure you've got a believable set of extenuating circumstances that make it kosher.
Sorry if that was a lot to throw at you at once, but I do think you've got an interesting concept here and I'd like to see it succeed. I'm a huge sucker for mystery stories, after all. ;) Good luck with it.